John Lightfoot on Matthew 1:8

[And Joram begat Ozias.] The names of Ahazias, Joash, and Amazias, are struck out. See the history in the books of the Kings, and 1 Chronicles 3:11, 12.

I. The promise that "the throne of David should not be empty," passed over, after a manner, for some time into the family of Jehu, the overthrower of Joram's family. For when he had razed the house of Ahab, and had slain Ahaziah, sprung, on the mother's side, of the family of Ahab, the Lord promiseth him that his sons should reign unto the fourth generation, 2 Kings 10:30. Therefore however the mean time the throne of David was not empty, and that Joash and Amazias sat during the space between, yet their names are not unfitly omitted by our evangelist, both because they were sometimes not very unlike Joram in their manners; and because their kingdom was very much eclipsed by the kingdom of Israel, when Ahazias was slain by Jehu, and his cousin Amazias taken and basely subdued by his cousin Joash, 2 Chronicles 25:23.

II. "The seed of the wicked shall be cut off," Psalm 37:28. Let the studious reader observe that, in the original, in this very place, the letter Ain, which is the last letter of wicked, and of seed, is cut off, and is not expressed; when, by the rule of acrostic verse (according to which this Psalm is composed), that letter ought to begin the next following verse.

III. "Thou shalt not make to thyself any graven image, &c. For I the Lord thy God am a jealous God; visiting the iniquity of the fathers upon the children, unto the third and fourth generation," (Exodus 20:5.

Joram walked in the idolatrous ways of the kings of Israel, according to the manner of the family of Ahab, 2 Kings 8:18. Which horrid violation of the second command God visits upon his posterity, according to the threatening of that command; and therefore the names of his sons are dashed out unto the fourth generation.

IV. The Old Testament also stigmatizeth that idolatry of Joram in a way not unlike this of the New; and shows that family unworthy to be numbered among David's progeny, 2 Chronicles 22:2: Ahazias, the son of two and forty years: that is, not of his age (for he was not above two-and-twenty, 2 Kings 8:26), but of the duration of the family of Omri, of which stock Ahazias was, on the mother's side; as will sufficiently appear to him that computes the years. A fatal thing surely! that the years of a king of Judah should be reckoned by the account of the house of Omri.

V. Let a genealogical style not much different be observed, 1 Chronicles 4:1; where Shobal, born in the fifth or sixth generation from Judah, is reckoned as if he were an immediate son of Judah. Compare chapter 2:50.

In the like manner, Ezra 7, in the genealogy of Ezra, five or six generations are erased.

[Please see Genealogies of the Bible: A Neglected Subject (111k) etc. at the Arthur Custance, Doorway Papers Library site regarding these lists and the "missing" names.]